

A299534


Solution b( ) of the complementary equation a(n) = b(n1) + 2*b(n2), where a(0) = 1, a(1) = 2; see Comments.


2



3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 83, 84, 85, 87, 88
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OFFSET

0,1


COMMENTS

From the BodeHarborthKimberling link:
a(n) = b(n1) + 2*b(n2) for n > 2;
b(0) = least positive integer not in {a(0),a(1)};
b(n) = least positive integer not in {a(0),...,a(n),b(0),...,b(n1)} for n > 0.
Note that (b(n)) is strictly increasing and is the complement of (a(n)).
See A022424 for a guide to related sequences.


LINKS

Table of n, a(n) for n=0..65.
JP. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254264.


MATHEMATICA

mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = b[n  1] + 2*b[n  2];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n  1}]]];
Table[a[n], {n, 0, 100}] (* A296220 *)
Table[b[n], {n, 0, 100}] (* A299534 *)


CROSSREFS

Cf. A022424, A296220.
Sequence in context: A039237 A039181 A298111 * A026454 A026458 A059109
Adjacent sequences: A299531 A299532 A299533 * A299535 A299536 A299537


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 21 2018


STATUS

approved



